1. Field of the Invention
The present invention relates to detection of data in a communications system, and, more particularly, to compensation for signal dispersion in an optical fiber.
2. Description of the Related Art
In many digital communications systems, a user generates digital information that is then processed into an encoded (e.g., error-correction encoded) and/or packetized stream of data. The stream of data is then divided into discrete blocks. Each of the blocks may be mapped onto a corresponding one of a sequence of code or symbol values (“symbols”) chosen from a pre-defined alphabet A, and generated with a period Ts, sometimes referred to as the “baud” rate. For optical transmission of the digital information, an optical carrier operating with a wavelength of, for example, 1310 nm or 1550 nm, is modulated with the encoded stream of data. The modulated optical carrier is then passed through an optical fiber, such as a single mode fiber (SMF) having its lowest order bound propagating at 1310 nm or 1550 nm.
The modulated optical signal transmitted through the optical fiber channel comprises a series of light pulses. Since a transmission medium may be modeled as a filter having a corresponding (frequency-domain) transfer function and (time-domain) impulse response, the pulse transmitted through the channel may have its shape modified based on this transfer function. The analog pulse shape may be modified in amplitude and phase, and also experience dispersion of the pulse. Consequently, the time duration of the pulse transmitted through a medium may extend over a period of time greater than the time duration of a particular symbol. Adjacent pulses transmitted through the medium may thus corrupt each other, which corruption is known as inter-symbol interference (ISI). This characteristic of the optical fiber (channel) is termed memory (e.g., if one adjacent pulse contributes to ISI, the memory “length” is one).
As bit rates in optical communication systems increase for high speed data transmission, such as rates above 10 Gbps, receivers are increasingly faced with mitigation of effects of pulse dispersion and ISI to the optical signal passing through the optical fiber channel. A receiver typically includes a detector forming decisions for received, sampled channel output data (“receive signal”) corresponding to the transmitted pulses. These detectors may apply compensation/equalization to the receive signal, and employ algorithms such as maximum-likelihood sequence detection to reconstruct the sequence of pulses in the transmitted, encoded stream of data.
For optical communication systems, there are several sources of pulse dispersion through an SMF. One source of dispersion is chromatic dispersion that causes time-domain pulse broadening due to the different traveling velocities of each of the optical pulse's spectral components. Prior art methods of compensation for chromatic dispersion use an opposite dispersion-compensating fiber (DCF) that has a greater dispersion parameter, usually by a factor of 10.
Another source of dispersion is polarization mode dispersion (PMD) that arises from imperfections in the circular symmetry of the fiber core. The imperfections typically are caused by manufacturing imperfections in the core, chemical impurities, and excessive bending or strain during installation. Imperfect circular symmetry results in birefringent SMF that causes two orthogonal principal polarization states (PPS) to propagate with different velocity through the fiber core. The resulting average differential group delay (DGD) is proportional to the square-root of the transmission distance. For example, an SMF having PMD of 10 ps/√{square root over (L)}, where L is the distance in kilometers, has a DGD of 100 ps at a distance of 100 km. A distances greater than 100 km and bit rates of greater than 10 Gbps, the DGD becomes significant when compared to the symbol period (Ts=100 ps at 10 Gbps). For a 10 Gbps transmission data rate, the magnitude of the maximum allowable value for the mean DGD τd between two orthogonal PPSs has an upper bound of 100 ps (i.e., τd≦100 ps). The (SMF) channel may be modeled as a two-symbol dispersive channel with impulse response h(t), and the model for a 10 Gbps channel that reflects statistical differential delay between the two PPS components may be as given in equation (1):h(t)=√{square root over (α)}(δ(t−τd))+√{square root over (1−α)}(δ(t))  (1)with δ(·) defined as the delta function, (α/(1−α)) defined as the power distribution ratio among the two orthogonal PPSs with 0<α<1, and where τd follows a Maxwell distribution as given in equation (2):
                                          P                          〈                              τ                d                            〉                                ⁡                      (                          τ              d                        )                          =                                                            32                ⁢                                                                  ⁢                                  τ                  d                  2                                                                              π                  2                                ⁢                                                      〈                                          τ                      d                                        〉                                    3                                                      ⁢                          exp              ⁡                              (                                  -                                                            4                      ⁢                                                                                          ⁢                                              τ                        d                        2                                                                                    π                      ⁢                                                                        〈                                                      τ                            d                                                    〉                                                2                                                                                            )                                      ⁢                                                  ⁢            0                    <                      τ            d                    <          ∞                                    (        2        )            
ISI results in multi-level channel output values due to the effect of the channel's memory on the binary input levels, causing degradation of a receiver's bit error rate (BER) performance. Linear ISI and time-varying PMD effects are generally compensated for using adaptive equalization.